On families of Hopf algebras without the dual Chevalley property

Naihong Hu,Rongchuan Xiong

doi:10.33044/revuma.v59n2a12

Abstract

Let k be an algebraically closed field of characteristic zero. We construct several families of finite-dimensional Hopf algebras over k without the dual Chevalley property via the generalized lifting method. In particular, we obtain 14 families of new Hopf algebras of dimension 128 with non-pointed duals which cover the eight families obtained in our unpublished version, arXiv:1701.01991 [math.QA].

Highlights

Let k be an algebraically closed field of characteristic zero
This work is a contribution to the classification of finite-dimensional Hopf algebras over k without the dual Chevalley property, that is, the coradical is not a subalgebra
More examples are needed to get a better understanding of the structures of such Hopf algebras

Summary

Introduction

Let k be an algebraically closed field of characteristic zero. This work is a contribution to the classification of finite-dimensional Hopf algebras over k without the dual Chevalley property, that is, the coradical is not a subalgebra. We determine all finite-dimensional Nichols algebras over simple objects in H YD Let A be a finite-dimensional Hopf algebra over H such that the corresponding infinitesimal braiding is a simple object W in H YD. We braidings and determine all finite-dimensional Nichols algebras over simple objects in we calculate the liftings of all finite-dimensional and prove Theorem A. We calculate the liftings of all finite-dimensional Nichols algebras and prove Theorem B

Preliminaries

On finite-dimensional Hopf algebras over H